The Interior City Infinity and Concavity in the No-Stop City (1970-1971)

In the late 60s it had become clear how the environment technification had allowed some typologies (supermarkets, car parks, factories) to reach potentially unlimited built depths becoming, therefore, independent from the outside. The No-Stop City is born from a very simple idea: to extend this technification to the totality of built reality encompassing, not only almost all functions, but ultimately, the whole city. This operation has paradoxical effects: as architecture grows, it loses most of the features that have traditionally defined it. A dissolution by hypertrophy that gives rise to an homogeneous, concave and potentially infinite space. But beyond the pure technical feasibility, there are two key influences, seemingly contradictory, that explain this endeavor for an interior and endless city: Marxism and Pop Art. The project is, in many senses, a built manifesto reflecting the militancy of the group members within the Italian Marxism. But it is also the embodiment of the groups declared interest in Pop Art, popular culture and mass society. The cross-influence of communism and consumerism explains this "quantitative utopia" in which the society and the factory, the production and consumption, would match. A city based on the centrality of consumer products and the subsequent loss of prominence of architecture, in which the urban phenomenon, while spreading endlessly over territory, ignoring its rural exteriority, dissolves the home as a sphere of privacy, ignoring its domestic interiority. A project, also in the wake of Marshall McLuhan, that illustrates like few others the conversion of the urbane into a virtually omnipresent "condition" and that still interrogates us with questions that are, on the other hand, eternal: What is a building? What is a city?

Bubble growth by injection of gas into viscous liquids in cylindrical and conical tubes.

The laminar low Mach number flow of a gas in a tube is analyzed for very small and very large values of the inlet-to-wall temperature ratio. When this ratio tends to zero, pressure forces confine the cold gas to a thin core around the axis of the tube. This core is neatly bounded by an ablation front that consumes it at a finite distance from the tube inlet. When the temperature ratio tends to infinity, the temperature of the gas increases smoothly from the wall to the axis of the tube and the shear stress and heat flux are positive at the wall despite the fact that the viscosity and thermal conductivity of the gas scaled with their inlet values tend to zero at the wall.

Laminar flow of a gas in a tube with large temperature differences.

The laminar low Mach number flow of a gas in a tube is analyzed for very small and very large values of the inlet-to-wall temperature ratio. When this ratio tends to zero, pressure forces confine the cold gas to a thin core around the axis of the tube. This core is neatly bounded by an ablation front that consumes it at a finite distance from the tube inlet. When the temperature ratio tends to infinity, the temperature of the gas increases smoothly from the wall to the axis of the tube and the shear stress and heat flux are positive at the wall despite the fact that the viscosity and thermal conductivity of the gas scaled with their inlet values tend to zero at the wall

Conexión con la meseta desde el Ebro medio de las vías romanas como base de la malla territorial de España

No tenemos conocimiento de ninguna red de caminos prerromanos que sirvieran como base de una posible malla territorial de España. Sin embargo, una sociedad prerromana sin caminos, por muy fragmentada y aislada que fuera, es algo improbable y mucho menos en la Edad del Hierro. Por eso en época prerromana existían infinidad de caminos, muchos de los cuales hoy han desaparecido y otros han sobrevivido, casi siempre con sus recorridos mejorados. Los pueblos prerromanos aprovecharon vías naturales de comunicación (ríos, vados, valles, puertos naturales, llanuras, etc.) para tender sus caminos. En sus orígenes no siguieron pautas concretas, si no que los caminos se originaban por el tránsito (de personas, ganados, mercancías, etc.) de un lugar a otro. De este modo la red viaria prerromana era caótica y anárquica: todo camino tenía numerosos ramales y variantes, según las necesidades. Pendientes excesivas, anchuras variables, etc., en decir eran vías espontáneas, surgidas sin ninguna planificación aparente. Los recorridos en general eran cortos, aunque algunas investigaciones actuales están demostrando que algunas de las cañadas ganaderas más importantes, como la Galiana, y de largo recorrido, eran de origen prerromano. En el caso de la península Ibérica, y más concretamente en el caso de la Meseta, el territorio estaba fragmentado en diversos pueblos y tribus, agrupados según criterios étnicos y culturales y con contactos con los pueblos próximos que motivan la preponderancia de caminos de recorrido cortos. Solo la necesidad de llevar los rebaños (de cabras y ovejas sobre todo) desde las serranías en verano a las llanuras en invierno, motivaría viajes más largos en los que algunas cañadas ganaderas jugarían un papel más importante. Con la llegada de los romanaos, se implantó en Hispania una densa red viaria, cuya construcción se prolongó durante toda la dominación romana, siendo reparadas muchas calzadas y vías en varias ocasiones. En época romana la red caminera era variada y estaba constituida por “las calzadas” que comunicaban puntos importantes, eran muy transitadas, de ahí que la administración romana las mantuviera siempre en buen estado, para asegurar el intercambio comercial entre zonas distintas, cobro de impuestos, etc. “Los caminos de tierra (viae terrenae)” que además de las calzadas, que podemos asemejar a las actuales carreteras de primer y segundo orden, constituían la infinidad de caminos locales y comarcales. Los trazados se realizaron unos en época romana, y otros muchos apoyándose en los caminos de la época prerromana, éstas vías no se realizaban buscando el recorrido más corto entre dos puntos, ni tampoco el más cómodo y con un firme estructural de menor importancia que en las calzadas. Tampoco estaban hechos para un tipo concreto de transporte, por lo que nos encontraríamos algunos que por su anchura permitían el paso de carros, y otros que sólo permitirían el paso a pie, a caballo o en burro. Solían ser, como hemos indicado, caminos de tierra con acabados en zahorras y recorridos en su mayor parte cortos y medianos. Dentro de la malla territorial de España las calzadas constituirían las denominadas “viae publicae” que constituían la red principal y esqueleto vertebrador de Hispania. Los caminos de tierra constituirían los denominados “actus” caminos de carácter regional que configuraban la mayor parte de la red. Muchas de las “viae publicae” y de los “actus” tendrían su origen en las “viae militares” que habrían sido los primeros construidos, apoyándose en muchas ocasiones en los caminos prerromanos, por los romanos para realizar la conquista de Hispania y que luego con la Paz romana habrían tenido otro tipo de uso. Dentro de estas “viae militares” tuvieron una importancia relevancia aquellas que se utilizaron en la conquista de la Celtiberia, culminada con la caída de Numantia. Dentro de ellas tuvo una importancia fundamental la vía romana del río Alhama, objeto de esta Tesis, que facilitaría el desplazamiento de los ejércitos romanos desde Graccurris, primera ciudad romana fundada en el Ebro medio, hasta Numantia. Desde la época Augusta, la vía romana del río Alhama, pasaría a formar parte de los denominados “actus” formando parte de la malla territorial de la Península Ibérica como vía de comunicación entre la Meseta y el Ebro Medio. We do not have knowledge of any network of ways prerromanos that were serving as base of a possible territorial mesh of Spain. Nevertheless, a company prerromana without ways, for very fragmented and isolated that was, is something improbable and great less in the Age of the Iron. Because of it in epoch prerromana existed infinity of ways, many of which today have disappeared and others have survived, almost always with his improved tours. The people prerromanos took advantage of natural routes of communication (rivers, fords, valleys, natural ports, plains, etc.) to stretch his ways. In his origins concrete guidelines did not continue, if not that the ways were originating for the traffic (of persons, cattle, goods, etc.) to and from. Thus the network viaria prerromana was chaotic and anarchic: all way had numerous branches and variants, according to the needs. Excessive slopes, variable widths, etc., in saying were spontaneous routes arisen without no apparent planning. The tours in general were short, though some current investigations are demonstrating that some of the most important cattle glens, as the Galiana, and of crossed length, were of origin prerromano. In case of the Iberian Peninsula, and more concretely in case of the Plateau, the territory was fragmented in diverse peoples and tribes, grouped according to ethnic and cultural criteria and with contacts with the near peoples that motivate the prevalence of short ways of tour. Only the need to take the flocks (of goats and sheeps especially) from the mountainous countries in summer to the plains in winter, would motivate longer trips in which some cattle glens would play a more important paper. With the arrival of the romanos, a dense network was implanted in Roman Spain viaria, whose construction extended during the whole Roman domination, being repaired many causeways and routes in several occasions. In Roman epoch the pertaining to roads network was changed and constituted by " the causeways " that were communicating important points, they were very travelled, of there that the Roman administration was supporting always in good condition, to assure the commercial exchange between different zones, collection of taxes, etc. "The dirt tracks (viae terrenae)" that besides the causeways, which we can make alike to the current roads of the first and second order, were constituting the infinity of local and regional ways. The tracings were realized some in Roman epoch, and great others resting on the ways of the epoch prerromana, these routes were not realized looking for the most short tour neither between points, two nor neither most comfortable and with a structural road surface of minor importance that in the causeways. They were not also done for a concrete type of transport, for what some of us would think that for his width they were allowing the step of cars, and others that only would allow the step afoot, astride or in donkey. They were in the habit of being, since we have indicated, dirt tracks with ended in zahorras and tours in his most short and medium. Inside the territorial mesh of Spain the causeways would constitute the called ones "viae publicae" that constituted the principal network and skeleton vertebrador of Roman Spain. The dirt tracks would constitute the "actus” called ways of regional character that were forming most of the network. Many of "viae publicae" and of the "actus" they would have his origin in " viae military" that would have been the first ones constructed, resting on many occasions on the ways prerromanos, for the Romans to realize the conquest of Roman Spain and that then with the Roman Peace they would have had another type of use. Inside these "viae military" had an importance relevancy those that were in use in the conquest of the Celtiberia, reached with Numantia's fall. Inside them a fundamental importance had the Roman route of the river Alhama, object of this Thesis, which would facilitate the displacement of the Roman armies from Graccurris, the first Roman city been founded on the average Ebro, up to Numantia. From the August epoch, the Roman route of the river Alhama, would happen to form a part of the "actus” forming a part of the territorial mesh of the Iberian Peninsula as road link between the Plateau and the Average Ebro.

Evidence for a disaggregation of the universe.

Combining the kinematical definitions of the two dimensionless parameters, the deceleration q(x) and the Hubble t 0 H(x), we get a differential equation (where x=t/t 0 is the age of the universe relative to its present value t 0). First integration gives the function H(x). The present values of the Hubble parameter H(1) [approximately t 0 H(1)≈1], and the deceleration parameter [approximately q(1)≈−0.5], determine the function H(x). A second integration gives the cosmological scale factor a(x). Differentiation of a(x) gives the speed of expansion of the universe. The evolution of the universe that results from our approach is: an initial extremely fast exponential expansion (inflation), followed by an almost linear expansion (first decelerated, and later accelerated). For the future, at approximately t≈3t 0 there is a final exponential expansion, a second inflation that produces a disaggregation of the universe to infinity. We find the necessary and sufficient conditions for this disaggregation to occur. The precise value of the final age is given only with one parameter: the present value of the deceleration parameter [q(1)≈−0.5]. This emerging picture of the history of the universe represents an important challenge, an opportunity for the immediate research on the Universe. These conclusions have been elaborated without the use of any particular cosmological model of the universe

Single optical surface imaging designs with unconstrained object to image mapping

In this work, novel imaging designs with a single optical surface (either refractive or reflective) are presented. In some of these designs, both object and image shapes are given but mapping from object to image is obtained as a result of the design. In other designs, not only the mapping is obtained in the design process, but also the shape of the object is found. In the examples considered, the image is virtual and located at infinity and is seen from known pupil, which can emulate a human eye. In the first introductory part, 2D designs have been done using three different design methods: a SMS design, a compound Cartesian oval surface, and a differential equation method for the limit case of small pupil. At the point-size pupil limit, it is proven that these three methods coincide. In the second part, previous 2D designs are extended to 3D by rotation and the astigmatism of the image has been studied. As an advanced variation, the differential equation method is used to provide the freedom to control the tangential rays and sagittal rays simultaneously. As a result, designs without astigmatism (at the small pupil limit) on a curved object surface have been obtained. Finally, this anastigmatic differential equation method has been extended to 3D for the general case, in which freeform surfaces are designed.

Combining a Similar Coefficient Identification Algorithm with the Boundary Element Method

The boundary element method (BEM) has been applied successfully to many engineering problems during the last decades. Compared with domain type methods like the finite element method (FEM) or the finite difference method (FDM) the BEM can handle problems where the medium extends to infinity much easier than domain type methods as there is no need to develop special boundary conditions (quiet or absorbing boundaries) or infinite elements at the boundaries introduced to limit the domain studied. The determination of the dynamic stiffness of arbitrarily shaped footings is just one of these fields where the BEM has been the method of choice, especially in the 1980s. With the continuous development of computer technology and the available hardware equipment the size of the problems under study grew and, as the flop count for solving the resulting linear system of equations grows with the third power of the number of equations, there was a need for the development of iterative methods with better performance. In [1] the GMRES algorithm was presented which is now widely used for implementations of the collocation BEM. While the FEM results in sparsely populated coefficient matrices, the BEM leads, in general, to fully or densely populated ones, depending on the number of subregions, posing a serious memory problem even for todays computers. If the geometry of the problem permits the surface of the domain to be meshed with equally shaped elements a lot of the resulting coefficients will be calculated and stored repeatedly. The present paper shows how these unnecessary operations can be avoided reducing the calculation time as well as the storage requirement. To this end a similar coefficient identification algorithm (SCIA), has been developed and implemented in a program written in Fortran 90. The vertical dynamic stiffness of a single pile in layered soil has been chosen to test the performance of the implementation. The results obtained with the 3-d model may be compared with those obtained with an axisymmetric formulation which are considered to be the reference values as the mesh quality is much better. The entire 3D model comprises more than 35000 dofs being a soil region with 21168 dofs the biggest single region. Note that the memory necessary to store all coefficients of this single region is about 6.8 GB, an amount which is usually not available with personal computers. In the problem under study the interface zone between the two adjacent soil regions as well as the surface of the top layer may be meshed with equally sized elements. In this case the application of the SCIA leads to an important reduction in memory requirements. The maximum memory used during the calculation has been reduced to 1.2 GB. The application of the SCIA thus permits problems to be solved on personal computers which otherwise would require much more powerful hardware.

Transition from isentropic to isothermal expansion in laser produced plasma

The transition that the expansion flow of laser-produced plasmas experiences when one moves from long, low intensity pulses (temperature vanishing at the isentropic plasma-vacuum front,lying at finite distance) to short, intense ones (non-zero, uniform temperature at the plasma-vacuum front, lying at infinity) is studied. For plznar geometry and lqge ion number Z, the transition occurs for dq5/dt=0.14(27/8)k712Z’1zn$/m4f, 12nK,,; mi, and K are laser intensity, critical density,ion mass, and Spitzer’s heat conduction coefficient. This result remains valid for finite Zit,h ough the numerical factor in d$/dt is different. Shorter wavelength lasers and higher 4 plasmas allow faster rising pulses below transition.

The theory of electrostatic probes in strong magnetic fields : Thesis submitted to the Faculty of The Graduate School of the University of Colorado for the Degree Doctor of Philosophy Department of Aerospace Engineering Science

A theory is developed of an electrostatic probe in a fully-ionized plasma in the presence of a strong magnetic field. The ratio of electron Larmor radius to probe transverse dimension is assumed to be small. Poisson's equation, together with kinetic equations for ions and electrons are considered. An asymptotic perturbation method of multiple scales is used by considering the characteristic lengths appearing in the problem. The leading behavior of the solution is found. The results obtained appear to apply to weaker fields also, agreeing with the solutions known in the limit of no magnetic field. The range of potentials for wich results are presented is limited. The basic effects produced by the field are a depletion of the plasma near the probe and a non-monotonic potential surrounding the probe. The ion saturation current is not changed but changes appear in both the floating potential Vf and the slope of the current-voltage diagram at Vf. The transition region extends beyond the space potential Vs,at wich point the current is largely reduced. The diagram does not have an exponential form in this region as commonly assumed. There exists saturation in electron collection. The extent to which the plasma is disturbed is determined. A cylindrical probe has no solution because of a logarithmic singularity at infinity. Extensions of the theory are considered.

Magnetic self-field effects on bare-tether current collection

It has been recently suggested that the magnetic field created by the current in a bare tether could sensibly reduce its electron collection capability in the magnetised ionosphere, a region of closed magnetic surfaces disconnecting the cylinder from infinity. In this paper, the ohmic voltage drop along the tether is taken into account in considering self-field effects. Separate analyses are carried out for the thrust and power generation and drag modes of operation, which are affected in different ways. In the power generation and drag modes, bias decreases as current increases along the tether, starting at the anodic, positively-biased end (upper end in the usual, eastward-flying spacecraft); in the thrust mode of operation, bias increases as current increases along the tether, starting at the lower end. When the ohmic voltage drop is considered, self-field effects are shown to be weak, in all cases, for tape tethers, and for circular cross-section tethers just conductive in a thin outer layer. Self-field effects might become important, in the drag case only, for tethers with fully conductive cross sections that are unrealistically heavy.